On Korn's first inequality for quadrilateral nonconforming finite elements of first order approximation properties
Result description
We investigate the Korn first inequality for quadrilateral nonconforming finite elements of first order approximation properties and clarify the dependence of the constant in this inequality on the discretization parameter h. Then we use the nonconforming elements for approximating the velocity in a discretization of the Stokes equations with boundary conditions involving surface forces and, using the result on the Korn inequality, we prove error estimates which are optimal for the pressure and suboptimal for the velocity.
Keywords
Korn'sfirstinequalityquadrilateralnonconformingfiniteelementsfirstorderapproximationproperties
The result's identifiers
Result code in IS VaVaI
Result on the web
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DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
On Korn's first inequality for quadrilateral nonconforming finite elements of first order approximation properties
Original language description
We investigate the Korn first inequality for quadrilateral nonconforming finite elements of first order approximation properties and clarify the dependence of the constant in this inequality on the discretization parameter h. Then we use the nonconforming elements for approximating the velocity in a discretization of the Stokes equations with boundary conditions involving surface forces and, using the result on the Korn inequality, we prove error estimates which are optimal for the pressure and suboptimal for the velocity.
Czech name
O Kornově nerovnosti pro čtyřúhelníkové nekonformní konečné prvky s aproximačními vlastnostmi prvního řádu
Czech description
Vyšetřujeme první Kornovu nerovnost pro čtyřúhelníkové nekonformní konečné prvky s aproximačními vlastnostmi prvního řádu a vyjasňujeme závislost konstanty v této nerovnosti na diskretizačním parametru h. Potom aproximujeme nekonformními prvky rychlost vdiskretizaci Stokesových rovnic s okrajovými podmínkami zahrnujícími povrchové síly a, použitím výsledku o Kornově nerovnosti, dokazujeme odhady chyb, které jsou optimální pro tlak a suboptimální pro rychlost.
Classification
Type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
GA201/05/0005: Mathematical theory and numerical simulation of problems of fluid mechanics
Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)
Others
Publication year
2005
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
International Journal of Numerical Analysis and Modeling
ISSN
0894-3370
e-ISSN
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Volume of the periodical
2
Issue of the periodical within the volume
4
Country of publishing house
GB - UNITED KINGDOM
Number of pages
20
Pages from-to
439-458
UT code for WoS article
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EID of the result in the Scopus database
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Result type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP
BA - General mathematics
Year of implementation
2005